The present invention relates generally to optical communications, and more particularly, to optimal combined 2R/3R regenerators placement method for line network topologies in optical WDM networks.
In optical transmission, the signal quality deteriorates due to the accumulation of linear and non-linear impairments as the signal traverses fiber spans and intermediate nodes. To keep the bit error rate (BER) below a certain threshold at the destination, the optical signal needs to be regenerated at intermediate nodes. Conventionally, optical-electrical-optical (O-E-O) 3R regenerators are used to achieve Reamplification, Reshaping, and Retiming of the signal. 3R regeneration may be complemented through the use of forward error correction (FEC) to further reduce bit errors.
In recent years, all-optical 2R regenerators have been developed, which provide an alternative solution for regenerating signals. These regenerators perform only reamplification and reshaping functions through optical layer processing, and therefore have lower cost and are more energy efficient due to the elimination of electrical modules. Another attractive feature is that 2R regenerators can regenerate multiple WDM channels simultaneously, further reducing hardware and operation cost. However, because all-optical 2R regenerators do not have clock recovery capability, and thus, cannot suppress timing jitter induced by intra-channel cross-phase modulation during transmission [2], the signal deteriorates faster than with 3R regeneration. Therefore, the solution that provides the best combination of performance and economy is one that utilizes both 2R and 3R regeneration. An open challenge is how to place 2R and 3R regenerators effectively in the network such that the benefits of all-optical regeneration can be leveraged maximally.
FIG. 1 shows the basic building blocks of an all-optical 2R regenerator [3]. A 2R regenerator consists of an optical amplifier that provides re-amplification capability, a filter that isolates a channel that needs to be regenerated, a passive reshaping nonlinear element that is responsible for reshaping the optical signal, and a variable attenuator that balances the output launched power between multiple optical channels.
Approximation of non-linear transfer function of a reshaping element by a piecewise linear function evolves the mean power and noise of an optical signal as shown in the following equations.Pouti=γ(Pini+PASEi)+(1−γ)Pi σouti2=γ(σini2+σASEi2)where Pini and Pouti represent the input and output mean power at signal level iε{0, 1} respectively. Similarly, σin,i2 and σout,i2 represent the input and output mean noise at signal level i. PASEi and σASE,i2 are the ASE noise power and ASE noise variance added by the amplifier. γ is the nonlinear parameter, and Pi is the power level at ith signal. Assuming a noise with Gaussian distributions, the BER at signal level 0 and 1 can be determined using an error function as shown in the equation immediately below. Finally, the average BER among different signal levels represents the BER of at the output of 2R regenerator.
      BER    i    =            (              1                              2            ⁢            π                              )        ×          (                        σ                      out            i                                                                        P              th                        -                          P              out              i                                                    )        ×          ⅇ                                    (                                          P                th                            -                              P                out                i                                      )                    2                          2          ⁢                      σ                          out              i                        2                              
The mixed 2R/3R regenerators' placement problem is formally defined as follows. We are given a physical topology G(V;E), where V is a set of ROADM nodes and E is a set of fibers connecting pairs of ROADM nodes. The distance between each pair of ROADM nodes (i, j) is represented in terms of the number of spans Kij, where a span is a segment of a fiber between consecutive amplifiers. The costs of 2R and 3R regenerators are C2R and C3R respectively. Sensitivity of a receiver in terms of minimum acceptable BER is represented as BERth. We need to place 2R and 3R regenerators along the given route Usd of the traffic demand R(s, d) between source s and destination d such that the cost is minimized. We assume that the network operates at a single line rate, and regenerators are only placed at ROADM nodes.
In a prior work, the author addresses the mixed 2R and 3R regenerator placement problem with the objective of minimizing the number of 3R regenerators irrespective of the costs of 2R and 3R regenerators, and proposes a greedy procedure. The procedure places a predefined finite number of 2R regenerators such that the total number of 3R regenerators is minimized. The running time for the greedy procedure increases factorially with the number of nodes in the network. Thus, the procedure may not be practical for large networks. Furthermore, the procedure may not result an optimal solution. In contrast as detailed below, the present invention addresses the mixed 2R and 3R regenerators placement problem using dynamic programming, and propose an effective procedure for the first time. The proposed procedure finds an optimal placement of 2R and 3R regenerators, and the time required to solve the problem increases polynomially with the network size that is significantly less than the procedure proposed in the prior work.
Accordingly, there is a need for optimal method to place 2R and 3R regenerators along the route of a connection such that the total cost is minimized.